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  1. Generalizing Functional Completeness in Belnap-Dunn Logic.Hitoshi Omori & Katsuhiko Sano - 2015 - Studia Logica 103 (5):883-917.
    One of the problems we face in many-valued logic is the difficulty of capturing the intuitive meaning of the connectives introduced through truth tables. At the same time, however, some logics have nice ways to capture the intended meaning of connectives easily, such as four-valued logic studied by Belnap and Dunn. Inspired by Dunn’s discovery, we first describe a mechanical procedure, in expansions of Belnap-Dunn logic, to obtain truth conditions in terms of the behavior of the Truth and the False, (...)
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  • Analytic Tableaux for All of SIXTEEN 3.Stefan Wintein & Reinhard Muskens - 2015 - Journal of Philosophical Logic 44 (5):473-487.
    In this paper we give an analytic tableau calculus P L 1 6 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t, ⊧ f, ⊧ i, and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment (...)
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  • A Non-Inferentialist, Anti-Realistic Conception of Logical Truth and Falsity.Heinrich Wansing - 2012 - Topoi 31 (1):93-100.
    Anti-realistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a non-inferentialist but nevertheless anti-realistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is told about what is told about (...)
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  • An Expansion of First-Order Belnap-Dunn Logic.K. Sano & H. Omori - 2014 - Logic Journal of the IGPL 22 (3):458-481.
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  • Gentzenization of Trilattice Logics.Mitio Takano - 2016 - Studia Logica 104 (5):917-929.
    Sequent calculi for trilattice logics, including those that are determined by the truth entailment, the falsity entailment and their intersection, are given. This partly answers the problems in Shramko-Wansing.
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  • Completeness and Cut-Elimination Theorems for Trilattice Logics.Norihiro Kamide & Heinrich Wansing - 2011 - Annals of Pure and Applied Logic 162 (10):816-835.
    A sequent calculus for Odintsov’s Hilbert-style axiomatization of a logic related to the trilattice SIXTEEN3 of generalized truth values is introduced. The completeness theorem w.r.t. a simple semantics for is proved using Maehara’s decomposition method that simultaneously derives the cut-elimination theorem for . A first-order extension of and its semantics are also introduced. The completeness and cut-elimination theorems for are proved using Schütte’s method.
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  • Truth Values.Yaroslav Shramko - 2010 - Stanford Encyclopedia of Philosophy.
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